Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Three-way Combinatorial Interpretations of Rogers–Ramanujan Identities


Affiliations
1 Department of Mathematics, Yadavindra College of Engineering, Punjabi University, Guru Kashi Campus, Talwandi Sabo, India
2 School of Mathematics, Thapar Institute of Engineering and Technology, Patiala - 147004, India
     

   Subscribe/Renew Journal


Combinatorial interpretations of the Rogers–Ramanujan identities are provided in terms of n–color partitions. Further interpretations in terms of ordinary partitions are obtained by using bijective maps. These results lead to the interpretations of two fifth order mock theta functions by attaching weights.


Keywords

Partitions, n–color partitions, mock theta functions, Rogers–Ramanujan identities.
Subscription Login to verify subscription
User
Notifications
Font Size


  • A. K. Agarwal, Rogers-Ramanujan identities for n–color partitions, J. Number Theory, 28(3) (1988), 299–305.
  • A.K. Agarwal, Lattice paths and n–color partitions, Util. Math., 53 (1998), 71–80.
  • A. K. Agarwal and G. E. Andrews, Rogers-Ramanujan identities for partitions with “N copies of N”, J. Combin. Theory Ser. A, 45(1) (1987), 40–49.
  • A.K. Agarwal and M. Rana, New combinatorial versions of G¨ollnitz–Gordon identities, Util. Math., 79 (2009), 145–155.
  • K. Alladi, Partition identities involving gaps and weights, Trans. Amer. Math. Soc., 349(12) (1997), 5001–5019.
  • P. A. MacMahon, Combinatory Analysis, volume 2, Cambridge Univ. Press, London and New York, 1916.
  • S. Sharma and M. Rana, Combinatorial interpretations of mock theta functions by attaching weights, Discrete Math., 341(7) (2018), 1903–1914.
  • S. Sharma and M. Rana, On mock theta functions and weight-attached Frobenius partitions, Ramanujan J., 50 (2019), 289–303.

Abstract Views: 185

PDF Views: 0




  • Three-way Combinatorial Interpretations of Rogers–Ramanujan Identities

Abstract Views: 185  |  PDF Views: 0

Authors

S Sharma
Department of Mathematics, Yadavindra College of Engineering, Punjabi University, Guru Kashi Campus, Talwandi Sabo, India
M Rana
School of Mathematics, Thapar Institute of Engineering and Technology, Patiala - 147004, India

Abstract


Combinatorial interpretations of the Rogers–Ramanujan identities are provided in terms of n–color partitions. Further interpretations in terms of ordinary partitions are obtained by using bijective maps. These results lead to the interpretations of two fifth order mock theta functions by attaching weights.


Keywords


Partitions, n–color partitions, mock theta functions, Rogers–Ramanujan identities.

References





DOI: https://doi.org/10.18311/jims%2F2022%2F29312